In particular, the article about superconductivity provides a rather general sketch about the phase diagram for a typical high Tc super conductor and discusses experimental support for the idea quantum criticality in standard sense and thus defined only at zero temperature could be crucial for the understanding of high Tc super conductivity.
The cuprates doped with holes by adding atoms binding some fraction of conduction electrons are very rich structured. The transition from antiferromagnetic insulator to ordinary metal involves several steps described by a 2-D phase diagram in the plane defined by temperature and doping fraction. Besides high Tc super conducting region the phases include pseudogap region, a region allowing charge oscillations, strange metal region, and metal region.
The attempt to find a unifed TGD based view about these conductivities led to an article I consider the general vision based on magnetic flux tubes carrying the dark heff/h=n variants of electrons as Cooper pairs or as free electrons allowing to understand not only high Tc super-conductivity and various accompanying phases but also exotic variants of conductivity associated with strange and bad metals, charge density waves and spin density waves. One should also understand the anomalous conductivity of SmB6, and the fact that electron currents in graphene behave more like viscous liquid current than ohmic current (see this).
The TGD inspired model for the anomalous conductivity of SmB6 as flux tube conductivity developed during last year forms an essential element of the mode. This model implies that Fermi energy controlled by the doping fraction would serve as a control variable whose value determines whether electrons can be transferred to magnetic flux tubes to form cyclotron orbits at the surface of the tube.
Also the metals (such as graphene) for which current behaves more like a viscous flow rather than Ohmic current can be understood in this framework: the liquid flow character comes from magnetic field which is mathematically like incompressible liquid flow. The electric field at flux tube space-time sheets is parallel to the flux tube and can reverse its direction since flux tubes resemble liquid flow and only the average of the flux tube electric field is is parallel to the applied electric field.
The outcome is a unified view about various conductivities relying on universal concepts and mechanisms. For a detailed representation see the article About high Tc superconductivity and other exotic conductivities.
For a summary of earlier postings see Links to the latest progress in TGD.